Solve {left(sqrt{25-(frac{20sqrt{17}}{17}}right)}^2

$${ \left( \sqrt{ 25-( \frac{ 20 \sqrt{ 17 } }{ 17 } } \right) }^{ 2 }$$

Evaluate

$$-\frac{20\sqrt{17}}{17}+25\approx 20.149287499$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{17}{17}.

$$\left(\sqrt{\frac{25\times 17}{17}-\frac{20\sqrt{17}}{17}}\right)^{2}$$

Since \frac{25\times 17}{17} and \frac{20\sqrt{17}}{17} have the same denominator, subtract them by subtracting their numerators.

$$\left(\sqrt{\frac{25\times 17-20\sqrt{17}}{17}}\right)^{2}$$

Do the multiplications in 25\times 17-20\sqrt{17}.

$$\left(\sqrt{\frac{425-20\sqrt{17}}{17}}\right)^{2}$$

Calculate \sqrt{\frac{425-20\sqrt{17}}{17}} to the power of 2 and get \frac{425-20\sqrt{17}}{17}.

$$\frac{425-20\sqrt{17}}{17}$$